The Center of Mass of a Thin Plate (region) Consider the region in the zy-plane bounded by the curve f(x) = 9 – 2 and the coordinate axis (see applet below). We can begin to find the center of mass of the thin plate (region) by dividing the region into thin rectangles orientated vertically. We then find the center of mass of each rectangle. For vertical rectangles, the center of mass of the rectangle is located at the point (2, 9) = (2, ). This leads to the formation of a Riemann sum and ultimately to a definite integral. Use the applet below to help in answering the questions that follow. (æ, f(x)) f(æ) 2 Suppose that the density of the thin plate is a constant p = 1. If vertical rectangle are used to construct the definite integral that describes the moments of the thin plate about the z and y axis then, The mass of the thin plate is M = The moment of the thin plate with respect to the z-axis is М, — The moment the thin plate with respect to the y-axis is м, — The center of mass the thin plate (region) is (2, 9) Note: your answer should be an ordered pair.

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